I am a Computer Engineering Student. I have watched all your videos and discovered that your videos are the best in the topic. I was really upset seeing no recent uploads. Glad to see you are uploading again. All the Best Bro and keep continuing your work because you are making an Impact.🤗🤗
For conditionals, another logic term that's commonly used when the Proposition is false (the statement that goes with the "If" part) is that we say the Conditional is "Vacuously True". For example, if I have the conditional statement "If I get an A on this exam, then the reason must be that I studied hard", it follows that this statement would be vacuously true if it turns out the proposition is false (the "I get an A" part). To continue the example, if I actually got a different grade like a B on the exam, then the statement is still, oddly, 'vacuously' true since the only way to disprove it would be for me to get an A for a reason other than studying hard (like maybe cheating off of other people!).
Is it equivalent to the "Implication" example that he gave, in which (A --> B) is still "True" when A is false? i.e. (A --> B) is "Vacuously True" when A is False? Edit 1: I think it's applicable in programming too, in the "Else" statement, for example: if (student.grade == 'A') then { print("You have studied hard."); } else { print("You might have studied hard,"); print("but try sleeping more before taking exams."); }
I learnt a lot of those statement overy life, but never thought of 'If and Only If' as being bidirectional. Now that you mentioned it, it looks so obvious!
Is “if and only if” actually bidirectional though? For example: suppose I have a variety of shapes. Some are circles and some are squares. I take some, but not all of the circles and put them in a box. It is true to say “A shape is in the box if and only if it is a circle” but not true to say “a shape is a circle if and only if it is in the box”. In other words, P is the shape being a circle, Q is being in the box. In this case, Q IFF P is true, but P IFF Q is not true. Edit: I have realized my mistake, but I’ll leave this up in case someone else is having the same question. The first condition is not actually “if and only if”. Rather it is simply “only if” The shape is in the box *only if* it is a circle. Which implies that a shape is a circle *if* it is in the box. But it is false to say “the shape is in the box if it is a circle” which means we cannot say “if *and* only if”. We can only say “only if”
I was having a hard time understanding the logics of implication, the colorful robots helped me a lot to understand the topic completely! I loved the video.
For a better understanding and simpler/eased calculation logic statements are comparable with venn diagrams and sets like compare negation with complement, conjunction with union and disjunction with interaction and you are good to go.
Hah, yesterday I had this exact subject. I had a hard time understanding equivalence so I looked at the truth table and calculated that it would be equal to ¬P∨Q to help me unferstand how it works, as logic gates are pretty easy to understand. This video helped me understand it clearly. Also pretty much all of this logic can be written as logic gates. Biconditional is just an NXOR, for example.
Not sure if you got a shadowban or something but these videos are 3blue1brown level enjoyable. Me: "yeah. I wonder whats the equivalent of (p exclusive or q)" Answer: " (10 or 01)" Me: 💀
Years ago I wanted to make AI using this logic. I had no idea about neural networks and also I was just a kid lol But this video, even including robots, reminds me of that time. And it's pretty cool.
The content is excellent, but I found a better way to express the 4:50 Implication: If the robot is blue and the blue robot always has an antenna. So when the robot is blue, then it has an antenna.
No, Third one will be not P, so, False or Q, False False or false is false Last one will be Not P, so, False again or Q, True false or true So it will be true
Bro please make videos on regular basis you tube recommended me this channel and i think this is the most underrated channel,your channel will grow for sure
I got a bit confused in the terms used in the implication part (I am totally lay on this though, maybe it is obvious to others). To me, it is more intuitive to understand it as P->Q being a VALID or in INVALID logical statement in this context, instead of saying it is TRUE or FALSE. Because it being T or F has to do with the particular state of the variables P and Q, which is confusing to me. For example, in the truth table of P->Q, to me P = FALSE makes Q undetermined due to the dependence relation.
at 1:55 you are wrong: if P = "The robot is blue" then ~P is "It is not the case that the robot is blue". It is a common but silly fallacy to render ~P as Q = "The robot is not blue". Both P and Q imply that the robot exists, but if there is no such robot referenced then P and Q are both false. But of course if P is false then ~P is true, and so clearly ~P != Q.
Classical Sentence Calculus is like football bets. Logic gets to your mind all by itself. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-supEdKORfNw.html (English subtitles)
thats seems to be quite complicated is there a symbol to represent every combination of your truth table and if so why use extra made up symbols? why not number with like a mark or something 🙃
I only properly understood implication when I saw P -> Q = ¬P \/ Q. Unfortunately, you kind of glossed over why they're equivalent and just showed the truth tables. They're equivalent because P -> Q means "if P is true then Q is also true" and is itself a logical statement which can be true or false. In ¬P \/ Q we see that when P is true ¬P is false so Q must be true to make the whole expression true; if a robot is blue then it must have an antenna otherwise the statement "if a robot is blue it has an antenna" is false. When P is false ¬P is true so Q can be either true or false; if a robot is not blue then it can either have an antenna or not have an antenna, either way it doesn't invalidate the statement that blue robots have antennae because it's not a blue robot. It's also useful to consider ¬P \/ Q in terms of Q, if Q is true then ¬P can be either true or false; if a robot has an antenna then it can be either blue or not blue and if Q is false then ¬P must be true and the robot must not be blue.
